ยง 51. Filling  vacancies by open competitive examination. 1.  Upon the
  written request of the appointing officer stating his reasons  therefor,
  or  on  its  own  initiative,  the  state  civil  service  department or
  appropriate municipal  commission  may  determine  to  conduct  an  open
  competitive  examination for filling a vacancy or vacancies instead of a
  promotion examination.
2. Except where the state  civil  service  department  or  appropriate
  municipal  commission  finds  that  there  are  less  than three persons
  eligible for promotion in the promotion unit where the  vacancy  exists,
  or  in  the  department,  if such vacancy is not in a separate promotion
  unit, and except where the department or municipal commission determines
  to  conduct  an   open   competitive   and   a   promotion   examination
  simultaneously,  a  notice of intention to conduct such open competitive
  examination or a copy of  the  appointing  officer's  request  for  open
  competitive  examination,  as  the  case  may  be, shall be publicly and
  conspicuously posted in the offices of both the appointing  officer  and
  the  state  civil service department or appropriate municipal commission
  and such request shall not be acted upon  until  said  notice  has  been
  posted as aforesaid for a period of not less than fifteen days.
3. Any  employee  who  believes that a promotion examination should be
  held for filling such vacancy may submit  to  the  state  civil  service
  department  or appropriate municipal commission his request, in writing,
  for a promotion examination rather than an open competitive examination,
  stating the reasons why he believes it to  be  practicable  and  in  the
  public interest to fill the vacancy by promotion examination.
Structure New York Laws
Article 4 - Recruitment of Personnel
Title A - Examinations and Eligible Lists
50-A - Test Validation Boards.
50-C - Discrimination Based Upon History of Cancerous Condition Prohibited.
51 - Filling Vacancies by Open Competitive Examination.
55 - Examination of Blind or Physically Handicapped Applicants.
55-A - Employment of Persons With Disabilities by Municipalities.
55-B - Employment of Persons With Disabilities by the State.
55-C - Employment of Veterans With Disabilities by the State.
55-C*2 - Acceptability of Certain High School Diplomas.
56 - Establishment and Duration of Eligible Lists.
57 - Continuous Recruitment for Certain Positions.
58 - Requirements for Provisional or Permanent Appointment of Certain Police Officers.
58-A - Requirements for Provisional or Permanent Appointment of Certain Fire Fighters.
59 - Placement of County Sheriffs' Personnel in Classified Service.
59-A - Placement of Detectives and Investigators in Classified Service.
59-B - Promotions of Supervisory Personnel of the Emergency Medical Service.
59-C - State Employment of Persons and Veterans With Disabilities Study.